have you tried having a look at the LWJGL Demos
to draw a cube at a different z level.
Either create 2 cubes with different z values (not what you want), or simply translate the mesh then re draw it.
notice the model translate method in the code:
-15.0f + xx * 3.0f,
-15.0f + yy * 3.0f,
0.0f) // <-- change this value here to effect the position on the z-axis
time + xx * 0.21f,
time + yy * 0.37f,
keep in mind that the example demo sets the limit of the depth range to 0.1 - 100 if your second cube is positioned outside of this range from the camera view it will not display